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lfunc_lfunctions • Show schema
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{'Lhash': '3196162390992173550365064514574', 'a10': [1.5702338143899117, 3.7145527431262524], 'a2': [-0.1744317384564385, 1.403414966650657], 'a3': [1.0921790525671786, -1.3443009027496262], 'a4': [-1.9391471372381293, -0.4896002248173175], 'a5': [2.4695801500447594, -1.4258127644136982], 'a6': [1.6961013157558158, 1.7672691721102902], 'a7': [-1.0203167421013688, -2.4410968325299285], 'a8': [1.0253610894554226, -2.6360262965742183], 'a9': [-0.6142898342669197, -2.9364345726605796], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.341486753957511, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.1744317384564385, -1.403414966650657]]], [3, [[1.0, 0], [-1.0921790525671786, 1.3443009027496262]]], [7, [[1.0, 0], [1.0203167421013688, 2.4410968325299285]]]], 'bad_primes': [2, 3, 7], 'central_character': '168.101', 'coefficient_field': 'CDF', 'conductor': 168, 'conductor_radical': 42, 'conjugate': 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'4.98607615844171756632715325076178', '6.08865146935374269864767448675623', '8.191503434074307025402371796278963', '9.105277010721157580297198799791172', '9.751854858263090076152424851971744', '10.77103196358853908858373859187829', '11.41616560348109131263861017434527', '13.03464341573997116709456292645901'], 'prelabel': '2-168-168.101-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.1582256921505028, 'root_angle': 0.0022291878638583326, 'root_number': '0.9999754776935879 + 0.007003142971601418*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.00111459393193', 'prec': 54}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.52132755699143949528029524624', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.13829409214304153619179623152', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.98607615844171756632715325076', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.341486753957511, 'bad_primes': [2, 3, 7], 'central_character': '168.101', 'conductor': 168, 'conductor_radical': 42, 'degree': 2, 'index': 21, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/168/2/ba/c/101/11'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '2-168-168.101-c1-0-21', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-168-168.101-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.1582256921505028, 'root_angle': 0.0011145939319291663, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.52132755699143949528029524624', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3196162390992173550365064514574', 'Lhash_array': ['3196162390992173550365064514574'], 'label': '2-168-168.101-c1-0-21', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/168/2/ba/c/101/11'}